They showed her power during the teaser, and there's a lot more background on her in the minicomics.

Did they demonstrate her having a power during the ep and I missed it, or is she still an unknown quantity?

You may have missed the scene right before the previouslies, where they introduced her. She goes by the codename Wireless because she can basically interface with the Wi-Fi. All the electronic information that's beaming back and forth via satellites? She can read it. And she can also send it.

You may have missed the scene right before the previouslies, where they introduced her.

Yep, totally did. Bastards! Why they gotta go putting new stuff BEFORE the previouslies? That's bass-ackwards.

Breaking the formula just reminded me of Supernatural with their THEN and NOW and how much it throws me when they just do a normal teaser without any previouslies. I like the previouslies, dammit.

It's a good thing they introduced Hana in this episode, otherwise I'd have lots more to complain about.

Oh, definitely. But: they introduced two women, they killed two women... it leaves a bit of a bad taste in my mouth. Out of curiosity, I counted up everyone I could think of to see how the actual numbers stacked up. Here's my count so far:

Women with powers: 4 living, 3 dead
Men with powers: 11 living, 2 dead
Non-powered women with major or recurring roles: 4 living, 3 dead
Non-powered men with major or recurring roles: 6 living, 3 dead

That list doesn't include people I considered to be simply collateral damage (several of Sylar's and Jessica's unnamed victims). Also, I'm counting Niki/Jessica as one person, but I suppose you could argue that she counts for two!

I thought he was there with Eden when she mind-whammied Sylar so that Sylar's abilities could be blocked first,

Oh yeah. Hm, okay, so it seems he does have all-purpose blocking powers -- which makes him a lot more formidable than I'd thought!

Also, if he couldn't block Peter's and Claude's abilities, why bring him to New York?

I guess I figured Bennet liked to have him around in order to clean up after himself quickly whenever necessary.

He's Bennett's security blanket. He drags him everywhere. Without him, Bennett loses all the control he has over the people in his life. I expect to see him cracking up pretty soon, now that he's lost control of Claire, the most important one.

So, can Peter combine powers to move the bullet out of Simone and then heal her? Is Peter too powerful now?

I wonder if he'll have some sort of reaction to using the powers he used in Isaac's studio. Like, extreme hunger or exhaustion.

Peter can't heal other people, only himself.

But I wonder if he can use his empathy to project the healing ability elsewhere?

Am I right in thinking Peter can only use one power at a time? As in, can't fly while invisible?

we don't know. He probably doesn't know. He can barely concentrate enough to use one power, let alone two.